Abstract
In this article, we prove a Lichnerowicz estimate for a compact convex domain of a Kähler manifold whose Ricci curvature satisfies Ric for some constant . When equality is achieved, the boundary of the domain is totally geodesic and there exists a nontrivial holomorphic vector field.
We show that a ball of sufficiently large radius in complex projective space provides an example of a strongly pseudoconvex domain which is not convex, and for which the Lichnerowicz estimate fails.
Citation
Vincent Guedj. Boris Kolev. Nader Yeganefar. "A Lichnerowicz estimate for the first eigenvalue of convex domains in Kähler manifolds." Anal. PDE 6 (5) 1001 - 1012, 2013. https://doi.org/10.2140/apde.2013.6.1001
Information